Emphasize the "private" in private eye. A private investigator works in the private sector, meaning he works cases for private citizens and businesses rather than for government agencies, such as detectives who work for police departments. Working in the private sector means private eyes cannot obtain privileged government information, they are not required to share investigative clues with other investigators and they purchase their own firearms, surveillance equipment and other detection devices.
Avoid coincidences. Contrivances, such as clues appearing out of the blue, are a disservice to your private eye and the reader. Never fabricate accidents to help the private eye solve the case, nor concoct unsubstantiated thoughts, or intuition, that prove to be correct.
Crank up the danger. Readers love to see private eyes overcoming, as well as sometimes falling victim to, dangerous situations. Use threatening encounters -- from fistfights to car crashes -- to build story tension and provide insight to your private eye's character. By the end of your story, the antagonist places the private eye in mortal peril, which the private eye conquers through escape, physical battle or mental acumen.
Solve the crime. The private eye, both in fiction and real life, has keen observation and problem-solving skills, an innate curiosity and sees a job through to its completion. She understands the legal statutes affecting the crime she's investigating, expertly applies investigative techniques and tools and uses resources such as databases, court files and contacts within government departments.
Make your private eye a hero. As the author Raymond Chandler wrote about the private eye in literature, "He is the hero; he is everything." Your fictional private eye might wrestle with personal demons, engage in violence, even be victimized by malicious circumstances or people, but ultimately he is the hero of the story.